When asked what Thatcher would have done with regards to the current state of Anglo-Irish relations and Brexit, he said: "She would have said "It is quite intolerable that this whole question of the Northern Ireland border has come to dominate the proceedings".
Mrs May then travels to Brussels on Wednesday to address a dinner for the other 27 European Union leaders.
European Council President Donald Tusk has invited May to make a personal appeal to the leaders of the other 27 nations, who will then meet tomorrow at a dinner from which she is excluded, to discuss Brexit.
Officials on both sides have now all-but given up on a breakthrough this week, and are increasingly concerned that time is running out to get an agreement before the UK's exit in March, the people said, speaking on condition of anonymity because the talks are confidential. The EU said the process was expected to take a few more weeks, pushing the timeline for a deal into November at the earliest.
The EU's Brexit pointman Michel Barnier met his British counterpart Dominic Raab in Brussels on Sunday, but they failed to agree on a draft Brexit divorce arrangement as had been hoped.
"We are not there yet", he said.
"We are approaching the end of negotiations. The backstop will, unfortunately, be there until and unless something else is agreed", he said.
The Irish border is an acutely sensitive issue, with some fearing any return to customs checks and other controls could revive tensions between Northern Ireland's Irish Catholic community and its British U.K. Protestant one.
The EU has suggested that Northern Ireland should follow European regulations on customs protocols for goods and services after Britain leaves.
The EU has proposed a backstop that would mean Northern Ireland staying in the EU customs union, large parts of the single market and the EU VAT system.
Climate Change Could Make Beer Prices Double, Study Says
Only 17 per cent of the globe's barley is actually used in brewing; most is harvested as feed for livestock. Wealthy beer-loving nations, such as Canada, Belgium and Denmark, would see the sharpest price rises.
One proposal is to keep the United Kingdom inside the EU's customs union on a temporary basis, which would mean no new checks on goods passing from Northern Ireland to Ireland would be needed. "That's new. It hasn't been there before", he said.
Labour MP Ian Murray said: "I'm pleased that at Labour conference, party policy changed to support a People's Vote, but it's clear that was achieved despite a lack of support from Jeremy Corbyn".
Mr Roth made clear that Germany is alive to the problems Mrs May could face in getting any deal through Parliament, telling reporters: "I have the impression that it is hard to secure the appropriate parliamentary majority in Great Britain".
Britain is scheduled to leave the European Union in March, and the Bank of England has warned that economic chaos will follow if the sides fail to reach a deal. Tusk warned that chances of Britain leaving without a deal were higher than ever before.
She received a chilly reception on Monday from many of her MPs as she updated them on the latest impasse in the talks and she will attempt to keep senior ministers on board at their weekly Cabinet meeting on Tuesday.
The meeting had prompted some reports of possible resignations.
The EU is waiting for new proposals from Britain.
The leader of the Democratic Unionist Party of the Northern Ireland stressed on Monday, that there can not be any "economic barriers between Britain and N. Ireland".
Penny Mordaunt, the worldwide development secretary, added "everyone needs to calm down". "This is going to be a hard time, but the whole Cabinet is digging in to get the best deal for this country".
Germany exhorted May to come to the summit with a positive message that could kick-start the stalled talks.
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